Sample size tables
How many participants do you need? These tables give the minimum sample size for the most common designs at α = .05, computed with the exact power formulas G*Power uses. For any other combination, use the power analysis calculator.
Updated · By Bibin XavierSurvey sample size by population size and margin of error
| Population | ±3% (95%) | ±5% (95%) | ±10% (95%) | ±3% (99%) | ±5% (99%) | ±10% (99%) |
|---|---|---|---|---|---|---|
| 100 | 92 | 80 | 50 | 95 | 88 | 63 |
| 200 | 169 | 132 | 66 | 181 | 154 | 91 |
| 300 | 235 | 169 | 73 | 259 | 207 | 108 |
| 500 | 341 | 218 | 81 | 394 | 286 | 125 |
| 1,000 | 517 | 278 | 88 | 649 | 400 | 143 |
| 2,000 | 697 | 323 | 92 | 960 | 499 | 154 |
| 5,000 | 880 | 357 | 95 | 1,347 | 586 | 161 |
| 10,000 | 965 | 370 | 96 | 1,557 | 623 | 164 |
| 50,000 | 1,045 | 382 | 96 | 1,778 | 655 | 166 |
| 100,000 | 1,056 | 383 | 96 | 1,810 | 660 | 166 |
| 1,000,000 | 1,066 | 384 | 97 | 1,840 | 664 | 166 |
| Very large | 1,068 | 385 | 97 | 1,844 | 664 | 166 |
Completed responses needed to estimate a proportion, assuming the most conservative proportion of 50% and a finite population correction. Divide by your expected response rate to get the number of invitations. Calculate your own.
Independent-samples t-test: participants per group
| Effect size d | Power .80 | Power .90 | Power .95 |
|---|---|---|---|
| 0.2 (small) | 394 | 527 | 651 |
| 0.3 | 176 | 235 | 290 |
| 0.5 (medium) | 64 | 86 | 105 |
| 0.8 (large) | 26 | 34 | 42 |
| 1.0 | 17 | 23 | 27 |
| 1.2 | 12 | 16 | 20 |
Two-tailed α = .05, equal group sizes. Multiply by 2 for the total sample. Computed with the noncentral t (F) distribution, matching G*Power.
Paired-samples or one-sample t-test: number of pairs
| Effect size dz | Power .80 | Power .90 | Power .95 |
|---|---|---|---|
| 0.2 | 199 | 265 | 327 |
| 0.3 | 90 | 119 | 147 |
| 0.5 | 34 | 44 | 54 |
| 0.8 | 15 | 19 | 23 |
| 1.0 | 10 | 13 | 16 |
Two-tailed α = .05. dz is the mean difference divided by the SD of the differences.
One-way ANOVA: participants per group (power .80)
| Effect size f | 2 groups | 3 groups | 4 groups | 5 groups | 6 groups |
|---|---|---|---|---|---|
| 0.10 (small) | 394 | 323 | 274 | 240 | 215 |
| 0.25 (medium) | 64 | 53 | 45 | 40 | 36 |
| 0.40 (large) | 26 | 22 | 19 | 16 | 15 |
α = .05. Multiply by the number of groups for the total sample. For power .90, add roughly a third.
Pearson correlation: total sample size
| Correlation r | Power .80 | Power .90 | Power .95 |
|---|---|---|---|
| .1 | 783 | 1047 | 1294 |
| .2 | 194 | 259 | 320 |
| .3 | 85 | 113 | 139 |
| .4 | 47 | 62 | 76 |
| .5 | 30 | 38 | 47 |
Two-tailed α = .05, testing r against zero (Fisher z approximation).
Multiple regression (overall model test): total sample size, power .80
| Predictors | f² = .02 (small) | f² = .15 (medium) | f² = .35 (large) |
|---|---|---|---|
| 1 | 395 | 55 | 25 |
| 2 | 485 | 68 | 31 |
| 3 | 550 | 77 | 36 |
| 4 | 602 | 85 | 40 |
| 5 | 647 | 92 | 43 |
| 6 | 688 | 98 | 46 |
| 8 | 759 | 109 | 52 |
| 10 | 822 | 118 | 57 |
| 12 | 878 | 127 | 61 |
| 15 | 954 | 139 | 68 |
α = .05, test of R² against zero. f² = R² / (1 − R²); f² = .15 corresponds to R² ≈ .13.
Chi-square test: total sample size, power .80
| Degrees of freedom | w = .10 (small) | w = .30 (medium) | w = .50 (large) |
|---|---|---|---|
| 1 | 785 | 88 | 32 |
| 2 | 964 | 108 | 39 |
| 3 | 1091 | 122 | 44 |
| 4 | 1194 | 133 | 48 |
| 6 | 1363 | 152 | 55 |
| 8 | 1503 | 167 | 61 |
α = .05. For a contingency table, df = (rows − 1)(columns − 1).
PLS-SEM: minimum sample size by the inverse square root method
| Smallest path coefficient | Minimum N (α = .05) | Minimum N (α = .01) |
|---|---|---|
| .05 | 2473 | 4015 |
| .10 | 619 | 1004 |
| .15 | 275 | 447 |
| .20 | 155 | 251 |
| .25 | 99 | 161 |
| .30 | 69 | 112 |
Kock and Hadaya (2018): Nmin > (2.486 / |pmin|)² for 5% significance and 80% power. Use the smallest path you expect to be significant.
Choosing an effect size
Use the effect size reported by similar published studies or a pilot study. If there is none, Cohen’s (1988) conventions are a common fallback: d = .2, .5, .8; f = .10, .25, .40; r = .1, .3, .5; f² = .02, .15, .35; w = .1, .3, .5 for small, medium and large effects. Smaller effects need far larger samples.
Reporting your sample size justification
“An a priori power analysis indicated that 64 participants per group were needed to detect a medium effect (d = 0.50) with 80% power at α = .05 (two-tailed).” Plan for attrition and incomplete responses by inflating the target by 10–20%.
Frequently asked questions
What sample size do I need for a survey?
For a large population, about 385 completed responses give a ±5% margin of error at 95% confidence, and about 1,068 give ±3%. Smaller populations need fewer, as the table shows.
How many participants per group for a t-test?
To detect a medium effect (d = 0.5) with 80% power at α = .05, you need 64 per group (128 in total). A small effect (d = 0.2) needs 394 per group.
What sample size do I need for multiple regression?
For a medium effect (f² = .15) and 80% power, 3 predictors need 77 participants and 10 predictors need 118. Rules of thumb such as 10 cases per predictor are less accurate than a power analysis.
How do I calculate sample size for PLS-SEM?
The inverse square root method gives a minimum: with a smallest expected path of .20, you need at least 155 cases at 5% significance. A power analysis of the most complex regression in the model is an alternative.
Related tools
How to cite this table
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APA 7
Xavier, B. (2026). Sample size tables [Web page]. FreeStatisticalTools.com. https://freestatisticaltools.com/sample-size-table/
BibTeX
@misc{xavier_samplesizetable_2026,
author = {Xavier, Bibin},
title = {Sample size tables},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/sample-size-table/}
}